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User blog:Dimensional consciousness/The connection between string theory and loop quantum gravity
An effort to solve some of LQG’s own internal problems has led to the first surprising link with string theory. Physicists who study LQG lack a clear understanding of how to zoom out from their network of space-time chunks and arrive at a large-scale description of space-time that dovetails with Einstein’s general theory of relativity — our best theory of gravity. More worrying still, their theory can’t reconcile the special case in which gravity can be neglected. It’s a malaise that befalls any approach reliant on chunking-up space-time: In Einstein’s theory of special relativity, an object will appear to contract depending on how fast an observer is moving relative to it. This contraction also affects the size of space-time chunks, which are then perceived differently by observers with different velocities. The discrepancy leads to problems with the central tenet of Einstein’s theory — that the laws of physics should be the same no matter what the observer’s velocity. “It’s difficult to introduce discrete structures without running into difficulties with special relativity,” said Pullin. In a brief paper he wrote in 2014 with frequent collaborator Rodolfo Gambini, a physicist at the University of the Republic in Montevideo, Uruguay, Pullin argued that making LQG compatible with special relativity necessitates interactions that are similar to those found in string theory. That the two approaches have something in common seemed likely to Pullin since a seminal discovery in the late 1990s by Juan Maldacena, a physicist at the Institute for Advanced Study in Princeton, N.J. Maldacena matched up a gravitational theory in a so-called anti-de Sitter (AdS) space-time with a field theory (CFT — the “C” is for “conformal”) on the boundary of the space-time. By using this AdS/CFT identification, the gravitational theory can be described by the better-understood field theory. The full version of the duality is a conjecture, but it has a well-understood limiting case that string theory plays no role in. Because strings don’t matter in this limiting case, it should be shared by any theory of quantum gravity. Pullin sees this as a contact point. Herman Verlinde, a theoretical physicist at Princeton University who frequently works on string theory, finds it plausible that methods from LQG can help illuminate the gravity side of the duality. In a recent paper, Verlinde looked at AdS/CFT in a simplified model with only two dimensions of space and one of time, or “2+1” as physicists say. He found that the AdS space can be described by a network like those used in LQG. Even though the construction presently only works in 2+1, it offers a new way to think about gravity. Verlinde hopes to generalize the model to higher dimensions. “Loop quantum gravity has been seen too narrowly. My approach is to be inclusive. It’s much more intellectually forward-looking,” he said. But even having successfully combined LQG methods with string theory to make headway in anti-de Sitter space, the question remains: How useful is that combination? Anti-de Sitter space-times have a negative cosmological constant (a number that describes the large-scale geometry of the universe); our universe has a positive one. We just don’t inhabit the mathematical construct that is AdS space. AdS is at the moment the best hint for the structure we are looking for, and then we have to find the twist to get a positive cosmological constant.” He thinks it’s time well spent: “Though AdS doesn’t describe our world, it will teach us some lessons that will guide us where to go.” Coming Together in a Black Hole Verlinde and Pullin both point to another chance for the string theory and loop quantum gravity communities to come together: the mysterious fate of information that falls into a black hole. In 2012, four researchers based at the University of California, Santa Barbara, highlighted an internal contradiction in the prevailing theory. They argued that requiring a black hole to let information escape would destroy the delicate structure of empty space around the black hole’s horizon, thereby creating a highly energetic barrier — a black hole “firewall.” This firewall, however, is incompatible with the equivalence principle that underlies general relativity, which holds that observers can’t tell whether they’ve crossed the horizon. The incompatibility roiled string theorists, who thought they understood black hole information and now must revisit their notebooks. But this isn’t a conundrum only for string theorists. “This whole discussion about the black hole firewalls took place mostly within the string theory community, which I don’t understand,” Verlinde said. “These questions about quantum information, and entanglement, and how to construct a mathematical Hilbert space – that’s exactly what people in loop quantum gravity have been working on for a long time.” Meanwhile, in a development that went unnoted by much of the string community, the barrier once posed by supersymmetry and extra dimensions has fallen as well. A group around Thomas Thiemann at Friedrich-Alexander University in Erlangen, Germany, has extended LQG to higher dimensions and included supersymmetry, both of which were formerly the territory of string theory. More recently, Norbert Bodendorfer, a former student of Thiemann’s who is now at the University of Warsaw, has applied methods of LQG’s loop quantization to anti-de Sitter space. He argues that LQG can be useful for the AdS/CFT duality in situations where string theorists don’t know how to perform gravitational computations. Bodendorfer feels that the former chasm between string theory and LQG is fading away. “On some occasions I’ve had the impression that string theorists knew very little about LQG and didn’t want to talk about it,” he said. “But the younger people in string theory, they are very open-minded. They are very interested what is going on at the interface.” “The biggest difference is in how we define our questions,” said Verlinde. “It’s more sociological than scientific, unfortunately.” He doesn’t think the two approaches are in conflict: “I’ve always viewed theory and loop quantum gravity as parts of the same description. LQG is a method, it’s not a theory. It’s a method to think of quantum mechanics and geometry. It’s a method that string theorists can use and are actually using. These things are not incompatible.” Connecting Loop Quantum Gravity and String Theory via Quantum Geometry We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macroscopic geometry emerges and String Theory then becomes the \emph{effective} theory which describes the dynamics of that exoskeleton. The core of the argument rests on the claim that the Nambu-Goto action of String Theory can be viewed as the expectation value of the LQG area operator evaluated on the string worldsheet. A concrete result is that the string tension of String Theory and the Barbero-Immirzi parameter of LQG turn out to be proportional to each other. Sources String Theory Meets Loop Quantum Gravity Connecting Loop Quantum Gravity and String Theory via Quantum Geometry Category:Blog posts Category:Sacred geometry Blog